====== My Work ======

See also my [[http://scholar.google.ca/citations?user=kQon5jkAAAAJ | Google Scholar profile]] or my [[https://www.zotero.org/rikblok/items/collectionKey/2N7KR5QI/order/dateModified/sort/desc | Zotero library]].

===== Published =====

^ Note name               ^ Note text                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         ^
^ :ref:Doebeli07      ^ Michael Doebeli, Hendrik J. Blok, Olof Leimar, and Ulf Dieckmann. {{:ref:rik:doebeli07.pdf| Multimodal pattern formation in phenotype distributions of sexual populations.}}//Proc. R. Soc. B//, 274:347-57. doi:[[doi>10.1098/rspb.2006.3725]]. 2007.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ^
| Abstract                | <div smaller>  During bouts of evolutionary diversification, such as adaptive radiations, the emerging species cluster around different locations in phenotype space. How such multimodal patterns in phenotype space can emerge from a single ancestral species is a fundamental question in biology. Frequency-dependent competition is one potential mechanism for such pattern formation, as has previously been shown in models based on the theory of adaptive dynamics. Here, we demonstrate that also in models similar to those used in quantitative genetics, phenotype distributions can split into multiple modes under the force of frequency-dependent competition. In sexual populations, this requires assortative mating, and we show that the multimodal splitting of initially unimodal distributions occurs over a range of assortment parameters. In addition, assortative mating can be favoured evolutionarily even if it incurs costs, because it provides a means of alleviating the effects of frequency dependence. Our results reveal that models at both ends of the spectrum between essentially monomorphic (adaptive dynamics) and fully polymorphic (quantitative genetics) yield similar results. This underscores that frequency-dependent selection is a strong agent of pattern formation in phenotype distributions, potentially resulting in adaptive speciation.  </div>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |
| Keywords                | sympatric speciation; frequency-dependent selection; pattern formation; assortative mating; competition; recombination; evolutionary branching                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |
^ :ref:PinedaKrch07   ^ Mario Pineda-Krch, Hendrik J. Blok, Ulf Dieckmann, and Michael Doebeli. {{:ref:rik:pinedakrch07.pdf|A tale of two cycles - distinguishing quasi-cycles and limit cycles in finite predator-prey populations.}}//Oikos//, 116:53-64. doi:[[doi>10.1111/j.2006.0030-1299.14940.x]]. 2007.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           ^
| Abstract                | <div smaller>  Periodic predator-prey dynamics in constant environments are usually taken as indicative of deterministic limit cycles. It is known, however, that demographic stochasticity in finite populations can also give rise to regular population cycles, even when the corresponding deterministic models predict a stable equilibrium. Specifically, such quasi-cycles are expected in stochastic versions of deterministic models exhibiting equilibrium dynamics with weakly damped oscillations. The existence of quasi-cycles substantially expands the scope for natural patterns of periodic population oscillations caused by ecological interactions, thereby complicating the conclusive interpretation of such patterns. Here we show how to distinguish between quasi-cycles and noisy limit cycles based on observing changing population sizes in predator-prey populations. We start by confirming that both types of cycle can occur in the individual-based version of a widely used class of deterministic predator-prey model. We then show that it is feasible and straightforward to accurately distinguish between the two types of cycle through the combined analysis of autocorrelations and marginal distributions of population sizes. Finally, by confronting these results with real ecological time series, we demonstrate that by using our methods even short and imperfect time series allow quasi-cycles and limit cycles to be distinguished reliably.  </div>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
^ :ref:Killingback06  ^ Timothy Killingback, Hendrik J. Blok, and Michael Doebeli. {{:ref:rik:killingback06.pdf|Scale-free extinction dynamics in spatially structured host-parasitoid systems.}}//J. Theor. Biol.//, 241:745-50. doi:[[doi>10.1016/j.jtbi.2006.01.010]] 2006.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ^
| Abstract                | <div smaller>Much of the work on extinction events has focused on external perturbations of ecosystems, such as climatic change, or anthropogenic factors. Extinction, however, can also be driven by endogenous factors, such as the ecological interactions between species in an ecosystem. Here we show that endogenously driven extinction events can have a scale-free distribution in simple spatially structured host-parasitoid systems. Due to the properties of this distribution there may be many such simple ecosystems that, although not strictly permanent, persist for arbitrarily long periods of time. We identify a critical phase transition in the parameter space of the host-parasitoid systems, and explain how this is related to the scale-free nature of the extinction process. Based on these results, we conjecture that scale-free extinction processes and critical phase transitions of the type we have found may be a characteristic feature of many spatially structured, multi-species ecosystems in nature. The necessary ingredient appears to be competition between species where the locally inferior type disperses faster in space. If this condition is satisfied then the eventual outcome depends subtly on the strength of local superiority of one species versus the dispersal rate of the other.</div>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |
^ :ref:Blok00b        ^ Hendrik J. Blok. [[:ref:rik:blok00b| On the nature of the stock market: Simulations and experiments.]] PhD thesis, University of British Columbia, 2000. [[http://arxiv.org/abs/cond-mat/0010211| arXiv:cond-mat/0010211]]                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        ^
| Abstract                | <div smaller>Over the last few years there has been a surge of activity within the physics community in the emerging field of Econophysics - the study of economic systems from a physicist's perspective. Physicists tend to take a different view than economists and other social scientists, being interested in such topics as phase transitions and fluctuations.\\ In this dissertation two simple models of stock exchange are developed and simulated numerically. The first is characterized by centralized trading with a market maker. Fluctuations are driven by a stochastic component in the agents' forecasts. As the scale of the fluctuations is varied a critical phase transition is discovered. Unfortunately, this model is unable to generate realistic market dynamics. \\ The second model discards the requirement of centralized trading. In this case the stochastic driving force is Gaussian-distributed "news events" which are public knowledge. Under variation of the control parameter the model exhibits two phase transitions: both a first- and a second-order (critical).\\ The decentralized model is able to capture many of the interesting properties observed in empirical markets such as fat tails in the distribution of returns, a brief memory in the return series, and long-range correlations in volatility. Significantly, these properties only emerge when the parameters are tuned such that the model spans the critical point. This suggests that real markets may operate at or near a critical point, but is unable to explain why this should be. This remains an interesting open question worth further investigation. \\ One of the main points of the thesis is that these empirical phenomena are not present in the stochastic driving force, but emerge endogenously from interactions between agents. Further, they emerge despite the simplicity of the modeled agents; suggesting complex market dynamics do not arise from the complexity of individual investors but simply from interactions between (even simple) investors. \\ Although the emphasis of this thesis is on the extent to which multi-agent models can produce complex dynamics, some attempt is also made to relate this work with empirical data. Firstly, the trading strategy applied by the agents in the second model is demonstrated to be adequate, if not optimal, and to have some surprising consequences. \\ Secondly, the claim put forth by Sornette et al. that large financial crashes may be heralded by accelerating precursory oscillations is also tested. It is shown that there is weak evidence for the existence of log-periodic precursors but the signal is probably too indistinct to allow for reliable predictions.</div>  |
^ :ref:Blok99         ^ Hendrik J. Blok and Birger Bergersen. {{:ref:rik:blok99.pdf|Synchronous versus asynchronous updating in the "game of life"}}. //Phys. Rev. E//, 59:3876-9. doi:[[doi>10.1103/PhysRevE.59.3876]]. 1999.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            ^
| Abstract                | <div smaller>The rules for the "game of Life" are modified to allow for only a random fraction of sites to be updated in each time step. Under variation of this fraction from the parallel updating limit down to the Poisson limit, a critical phase transition is observed that explains why the game of Life appears to obey self-organized criticality. The critical exponents are calculated and the static exponents appear to belong to the directed percolation universality class in 2+1 dimensions. The dynamic exponents, however, are nonuniversal, as seen in other systems with multiple absorbing states.</div>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |
^ :ref:Blok97         ^ Hendrik J. Blok and Birger Bergersen. {{:ref:rik:blok97.pdf|Effect of boundary conditions on scaling in the "game of Life"}}. //Phys. Rev. E//, 55:6249-52. doi:[[doi>10.1103/PhysRevE.55.6249]]. 1997.                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           ^
| Abstract                | <div smaller>The debate as to whether the "game of Life" is self-organized critical remains unresolved. We present evidence that boundary conditions play an important role in the scaling behaviour, resulting in apparently contradictory results. We develop an analytic form for the scaling function and demonstrate that periodic boundaries force saturation, while open boundaries exhibit no such transitions on similar scales. We also consider the removal of boundaries altogether.</div>                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |








===== Presentations =====

^ Note name ^ Note text ^
^ :ref:Blok03 ^ Hendrik J. Blok. {{:ref:rik:blok03.pdf|Self-affine timeseries analysis.}} Guest lecture for U.B.C. Physics 510: Stochastic Processes in Physics, 2003. ^
| Abstract | <div smaller>A brief introduction to Lévy flight and fractional Brownian motion from the experimentalist's perspective. Simple tools to analyze these timeseries, the Zipf plot and dispersional analysis, are presented. As a demonstration, these tools are applied to financial and meteorological data to determine the Lévy and Hurst exponents.</div> |
^ :ref:Blok02b ^ Hendrik J. Blok. {{:ref:rik:blok02b.pdf|Rock, paper and scissors in space: A demonstration of R2DToo.}} SOWD Lab Meeting, Zoology, U.B.C., 2002. ^
| Abstract | <div smaller>Presentation given at the Dec. 2, 2002 SOWD Lab Meeting. A demonstration of how the simulation tool R2DToo can be used to solve real problems.</div> |
^ :ref:Blok02 ^ Hendrik J. Blok. {{:ref:rik:blok02.pdf|Statistical properties of financial timeseries.}} PIMS-MITACS Math Finance Seminar, U.B.C., 2002. ^
| Abstract | <div smaller>A brief introduction to Lévy flight and fractional Brownian motion from the experimentalist's perspective. Simple tools to analyze these timeseries, the Zipf plot and dispersional analysis, are presented. As a demonstration, these tools are applied to intraday foreign exchange data to determine the Lévy and Hurst exponents.</div> |
^ :ref:Blok01 ^ Hendrik J. Blok. {{:ref:rik:blok01.pdf|Can memes drive genes?}} Presentation for Emergent Phenomena discussion group, U.B.C., 2001. ^
| Abstract | <div smaller>Assuming culture is transmitted horizontally (via imitation) a model was constructed to determine the conditions under which culture can dominate genetic evolution ("get off the leash" according to Blackmore [Blackmore99]). Two requirements were found: (1) culture must compete with genes (required only for the effect to be empirically testable); and (2) Interactions between individuals must be confined to small groups or neighbourhoods. The model was tested via analysis and simulation. \\ In this talk I will present the model, analysis, and simulation results. Feedback is appreciated.</div> |
^ :ref:Blok00c ^ Hendrik J. Blok. {{:ref:rik:blok00c.pdf|On the nature of the stock market: Simulations and experiments.}} Final PhD oral defense, U.B.C., 2000. ^
^ :ref:Blok00 ^ Hendrik J. Blok. {{:ref:rik:blok00.pdf|On the nature of the stock market: Simulations and experiments.}} Departmental PhD oral defense, U.B.C., 2000. ^
^ :ref:Blok98b ^ Hendrik J. Blok. {{:ref:rik:blok98b.pdf|Extra! Extra! Critical update on 'Life'.}} Presentation for Peter Wall Inst. Adv. Science, Crisis Points Group, U.B.C., 1998. ^
^ :ref:rik:Blok98 ^ Hendrik J. Blok. {{:ref:rik:blok98.pdf|Modelling intentionality: The gambler.}} Presentation for Phys 510, U.B.C., 1998. ^


